Instantaneous Kinematics and Singularity Analysis of a Novel Three-legged Mobile Robot with Active S-r-r-r Legs

1 Copyright © 2008 by ASME 1. Address all correspondence to this author. ABSTRACT STriDER (Self-excited Tripedal Dynamic Experimental Robot) is a unique three-legged walking robot that utilizes its innovative tripedal gait to walk. Previous work on the kinematic analysis of STriDER mainly focused on solving the forward and inverse displacement problems. As a continuation, this paper addresses the instantaneous kinematics and singularity analysis. The kinematic configuration of STriDER is modeled as a three-legged in-parallel manipulator when all three feet of the robot are in contact with the ground without slipping. The results obtained from this study can be implemented to the velocity control and the resistance of disturbance forces, thus improving the motion accuracy and stability of the robot. By using screw theory, the screw-based Jacobian matrices of the manipulator can be derived since the forward displacement problems have already been solved. Based on these Jacobian matrices, the transformation equations from the active joint rates to the velocities of the body and vice versa are derived. Then, a complete investigation on the identification and elimination of singularities is presented. Unlike serial manipulators, in-parallel manipulators have two types of singularities, i.e., forward and inverse singularities. The inverse singularities are identified by checking the singular configurations of individual legs and the determinant of the inverse Jacobian matrix. By using Grassmann line geometry, the analytical conditions under which the forward singularities occur are obtained. A study on each case of these singular configurations shows that the redundant-actuation scheme of the active joints can effectively eliminate forward singularities.